The area of a solid of a box is 120 sq.cm.The area of the other sides of the box is 96 sq.cm.If the area of the upper surface of the box is 80 sq.cm.Find the volume of the box*1 point1) 800 cm32) 864cm33) 960 cm34) 720 cm3

To solve this problem, we need to understand that a box or a rectangular prism has 6 faces. The total surface area of the box is given by the sum of the areas of all these faces.

From the problem, we know that the total area of the box is 120 sq.cm + 96 sq.cm + 80 sq.cm = 296 sq.cm.

Since a box has 6 faces and each pair of opposite faces has the same area, we can divide the total surface area by 2 to find the area of one pair of opposite faces. So, 296 sq.cm / 2 = 148 sq.cm.

We know that the area of the upper surface of the box is 80 sq.cm. So, the area of the base of the box (which is the same as the upper surface) is also 80 sq.cm.

Now, we can subtract the area of the base from the total area of one pair of opposite faces to find the area of the front (or back) face of the box. So, 148 sq.cm - 80 sq.cm = 68 sq.cm.

The area of a rectangle (which is the shape of the front face of the box) is given by length x width. Since we know the area and one of the dimensions (the width is the same as the width of the base, which we can find by taking the square root of the area of the base), we can find the other dimension (the height of the box).

So, the height of the box is 68 sq.cm / sqrt(80 sq.cm) = 68 sq.cm / 8.94 cm = 7.6 cm (approximately).

Finally, the volume of a box is given by length x width x height. So, the volume of the box is sqrt(80 sq.cm) x sqrt(80 sq.cm) x 7.6 cm = 8.94 cm x 8.94 cm x 7.6 cm = 640.09 cm^3 (approximately).

So, the closest answer to the volume of the box is 640 cm^3. However, this option is not given in the choices. There might be a mistake in the problem or the choices given.